MELBOURNE, May 11 (Reuters) - Australian oil and gas company AWE Ltd said on Wednesday it had rejected a A$421 million ($311 million) takeover approach from U.S.-based private equity fund Lone Star, calling the offer too cheap.

Lone Star's Japan Acquisitions unit offered A$0.80 a share, a 30 percent premium to AWE's close on Tuesday.

"The board concluded that it is opportunistic and does not reflect the fair underlying asset value of the company," AWE said in a statement to the Australian stock exchange.

AWE's shares have slumped 58 percent over the past year, hammered like its peers by sliding oil and gas prices.

The company, which recently appointed a new chief executive, David Biggs, has stakes in oil and gas projects in Australia, China, Indonesia, New Zealand, and the United States. As of March 31, it had net cash of A$52 million and no debt.

Lone Star's U.S.-based spokesman was not immediately available to comment.

AWE's shares rose just 2.4 percent to A$0.63 on Wednesday, reflecting investors' doubts a higher offer would emerge.

($1 = 1.3545 Australian dollars) (Reporting by Sonali Paul; Editing by Stephen Coates)